Physics A2 unit 5, section 9.5 - radioactive decay

In this section:

• what is half-life?
• what do we mean by the activity of a radioactive isotope?
• what is meant by the half-life of a radioactive isotope?
• does anything affect radioactive decay?

Background Mathematical Knowledge:

• You will understand this section and the next two sections much better if you understand about exponentials and logarithms
• You can learn more about exponents and logs in A-level mathematics module C3 chapter 3
• Here is an outline to exponential functions, logs and the exponential function y = e x :

A simplified introduction to exponential functions.jnt

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Half Life

• When the nucleus of a radioactive isotope decays it emits an alpha or beta particle.
• This changes it into another element as we saw in section 9.3.
• So the number of radioactive nucleii decreases with time as does the mass of this particular isotope.
• A convenient way to express this reduction is by measuring the time it takes for the amount of the isotpe to reduce by half. This is the half-life.
• This produces a characteristic exponential decay curve:

• This means that the amount of the radioactive isotope never reaches zero, and it never completely stops emiting radioactive particles.
• At a time of 10 times the half-life, T, the amount of the isotope left is ½ × ½ × ½ × ½ × ½ × ½ × ½ × ½ × ½ × ½ of its original value.
• This is less than 0.1% since (½)10 = 1/1024
• Radioactive decay is a random process.
• We can model radioactive decay by repeatedly rolling dice:
  • Start with 1000 dice each of which represents a nucleus of a radio isotope X
  • When a particular die shows 1, this represents the radioactive decay of this particulr nucleus
  • The probability of any particular die showing 1 at any particular time is 1/6

radioactive decay model.xlsm

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• For more on the mathematics of approximating the probability of repeated independent events (rolling the dice) with the number of occurences of an event in continuous time (radioactive decay) see A-level mathematics S2 section 1.7 - The Poisson distribution as a model for the Binomial distribution.

Activity

Activity and Power

Homework

Homework hints

C3 Exercise 3A (using the exponential function).jnt

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